{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Function approximation with linear models and neural network\n",
    "* Are Linear models sufficient for approximating transcedental functions? What about polynomial functions?\n",
    "* Do neural networks perform better in those cases?\n",
    "* Does the depth of the neural network matter?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import basic libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global variables for the program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_points = 75 # Number of points for constructing function\n",
    "x_min = 1 # Min of the range of x (feature)\n",
    "x_max = 15 # Max of the range of x (feature)\n",
    "noise_mean = 0 # Mean of the Gaussian noise adder\n",
    "noise_sd = 10 # Std.Dev of the Gaussian noise adder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate feature and output vector following a non-linear function\n",
    "The ground truth or originating function is as follows:\n",
    "\n",
    "$$ y=f(x)= (20x+3x^2+0.1x^3).sin(x).e^{-0.1x}+\\psi(x) $$\n",
    "\n",
    "$$ {OR} $$\n",
    "\n",
    "$$ y=f(x)= (20x+3x^2+0.1x^3)+\\psi(x) $$\n",
    "\n",
    "$${where,}\\ \\psi(x) : {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Definition of the function with exponential and sinusoidal terms\n",
    "def func_trans(x):\n",
    "    result = (20*x+3*x**2+0.1*x**3)*np.sin(x)*np.exp(-0.1*x)\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Definition of the function without exponential and sinusoidal terms i.e. just the polynomial\n",
    "def func_poly(x):\n",
    "    result = 20*x+3*x**2+0.1*x**3\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Densely spaced points for generating the ideal functional curve\n",
    "x_smooth = np.array(np.linspace(x_min,x_max,501))\n",
    "\n",
    "# Use one of the following\n",
    "y_smooth = func_trans(x_smooth)\n",
    "#y_smooth = func_poly(x_smooth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Linearly spaced sample points\n",
    "X=np.array(np.linspace(x_min,x_max,N_points))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Added observational/measurement noise\n",
    "noise_x = np.random.normal(loc=noise_mean,scale=noise_sd,size=N_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Observed output after adding the noise\n",
    "y = func_trans(X)+noise_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Ideal y</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.588211</td>\n",
       "      <td>26.157284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.189189</td>\n",
       "      <td>23.232586</td>\n",
       "      <td>13.896885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.378378</td>\n",
       "      <td>28.672889</td>\n",
       "      <td>44.913735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.567568</td>\n",
       "      <td>33.434022</td>\n",
       "      <td>31.334087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.756757</td>\n",
       "      <td>37.046351</td>\n",
       "      <td>25.576298</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X    Ideal y          y\n",
       "0  1.000000  17.588211  26.157284\n",
       "1  1.189189  23.232586  13.896885\n",
       "2  1.378378  28.672889  44.913735\n",
       "3  1.567568  33.434022  31.334087\n",
       "4  1.756757  37.046351  25.576298"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the values in a DataFrame\n",
    "df = pd.DataFrame(data=X,columns=['X'])\n",
    "df['Ideal y']=df['X'].apply(func_trans)\n",
    "df['y']=y\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the function(s), both the ideal characteristic and the observed output (with process and observation noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e8e59a46a0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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IgQqxsS2BG4B44A5gVsC9Fay5CwduLqUlIiIi1VD+VCGLFmWQlTUeeANIpmbNlsya9RZz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\nHXgY+BjoYK29GYjDn6FUa1dddRUZGRn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MiIiR/OlPDzFu3Dg++eSTIltBld31Wp0jR37D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\nnIiIiEiQ+X8BwuiyT4VzMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8ed8050b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X','y',title='True process and measured samples\\n',\n",
    "                grid=True,edgecolors=(0,0,0),c='blue',s=60,figsize=(10,6))\n",
    "plt.plot(x_smooth,y_smooth,'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import scikit-learn librares and prepare train/test splits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import LassoCV\n",
    "from sklearn.linear_model import RidgeCV\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], test_size=0.33)\n",
    "\n",
    "X_train=X_train.values.reshape(X_train.size,1)\n",
    "y_train=y_train.values.reshape(y_train.size,1)\n",
    "X_test=X_test.values.reshape(X_test.size,1)\n",
    "y_test=y_test.values.reshape(y_test.size,1)\n",
    "\n",
    "from sklearn import preprocessing\n",
    "X_scaled = preprocessing.scale(X_train)\n",
    "y_scaled = preprocessing.scale(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model with LASSO/Ridge regularization (pipelined) with lineary spaced samples\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Alpha (regularization strength) of ridge regression\n",
    "ridge_alpha = tuple([10**(x) for x in range(-3,0,1) ])\n",
    "\n",
    "# Regularization strength parameters of LASSO regression\n",
    "lasso_eps = 0.0001\n",
    "lasso_nalpha=20\n",
    "lasso_iter=5000\n",
    "\n",
    "# Min and max degree of polynomials features to consider\n",
    "degree_min = 2\n",
    "degree_max = 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZAqNGVZY//jisv37z4zGrs1r6XDYClpTcX5LLulI7zq919cwF7HHGzWx+4nXs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f6fb5a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TT8LWW5eWr1gB63rgpnWWas5z+bKkm4HX56L3R8SM+obVvsqdiFhsrDvKW1pd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\nWc05uZiZWc39f90c4gpX5h0pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f5b64cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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etZYgjeS7gdTE/TfSxaz1GqbfEG4WMzOzmnPNxczMaq5pfS6SXkYafjoix3FlRJwmaRPS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\nnJOLmZnV3P8Hjy/I5W+N3/sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f72bce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fvhzW9tga6yzVnOfyJUk3A6/PRR+IiOn1Dat5ijviu4cNA1UlhUrnigyRnFgG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\nWc05uZiZWc05uZiZWc39f9vUljtLAoicAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f6fa47b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f6fab240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WvLZGdyytXsOqt5rWMu+/H/beu7TcTWDW4aqZW+wsoIs0auwyYDjwE2Cf+obW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\nZlZzTi5mZlZzTi5mZlZz/x+MLsit6qdTHgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f6ccb080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kjY6IGfUMzBrP41ElNW0avO8+2Guv0nI3gVmH6zW5SDoD6CKdNXYpMBT4ObB3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\n07UrZmb2OjeLVWP+fDj1VLj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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f6ccb518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Empty lists to store model data\n",
    "linear_sample_score = []\n",
    "poly_degree = []\n",
    "rmse=[]\n",
    "t_linear=[]\n",
    "\n",
    "import time\n",
    "# Iterate over increasing degree of polynomial complexity\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    t1=time.time()\n",
    "    model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "    #                                                              max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    t2=time.time()\n",
    "    t = t2-t1\n",
    "    t_linear.append(t)\n",
    "    y_pred = np.array(model.predict(X_train))\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(test_pred-y_test)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    linear_sample_score.append(test_score)\n",
    "    rmse.append(RMSE)\n",
    "    poly_degree.append(degree)\n",
    "    #print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "       \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1e8f7169fd0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X/frw73+H5D1F5swJIwDGjKn4cUWkQip9lj0zawAcCDybVvwg0Dp6zD8SOCW6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f522a0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(poly_degree,rmse,lw=3,c='red')\n",
    "plt.xlabel (\"\\nModel Complexity: Degree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"Root-mean-square error on test set\",fontsize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_score = pd.DataFrame(data={'degree':[d for d in range(degree_min,degree_max+1)],\n",
    "                              'Linear sample score':linear_sample_score})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t_linear=np.array(t_linear)\n",
    "time_linear=np.sum(t_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1e8f5b72d30>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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D9Qmq0qAB7LxzJhHYc0/YYovyxFsTtWwZkoC//CVcC+Cmm0JvC4RJle6+O9x6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\nEokqknKQSCQSiUSiiv8BNMl8WuLauXIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f7326668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(poly_degree,linear_sample_score,lw=3,c='red')\n",
    "plt.xlabel (\"\\nModel Complexity: Degree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"R^2 score on test set\",fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural network for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import and declaration of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural network parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.00001\n",
    "training_epochs = 100000\n",
    "\n",
    "n_input = 1  # Number of features\n",
    "n_output = 1  # Regression output is a number only\n",
    "\n",
    "n_hidden_layer = 25 # number of neurons in the hidden layer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights and bias variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Store layers weight & bias as Variables classes in dictionaries\n",
    "weights = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_input, n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_hidden_layer, n_output]))\n",
    "}\n",
    "biases = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_output]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the weights tensor of hidden layer: (1, 25)\n",
      "Shape of the weights tensor of output layer: (25, 1)\n",
      "--------------------------------------------------------\n",
      "Shape of the bias tensor of hidden layer: (25,)\n",
      "Shape of the bias tensor of output layer: (1,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of the weights tensor of hidden layer:\",weights['hidden_layer'].shape)\n",
    "print(\"Shape of the weights tensor of output layer:\",weights['out'].shape)\n",
    "print(\"--------------------------------------------------------\")\n",
    "print(\"Shape of the bias tensor of hidden layer:\",biases['hidden_layer'].shape)\n",
    "print(\"Shape of the bias tensor of output layer:\",biases['out'].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weight tensor initialized randomly\n",
      "---------------------------------------\n",
      " [[-0.27438638 -1.40927088  1.23991358  0.2628333   0.01353883 -1.29243374\n",
      "   1.98067057  2.48953533  1.40660822  2.25200438 -0.97263658 -0.12663926\n",
      "   0.60279024  0.87737107 -0.57692254 -0.51974356 -0.03162678  1.54640281\n",
      "   0.97244233 -0.6625039   0.52613646  1.91530299  2.17841697 -0.9945786\n",
      "  -0.66208237]]\n",
      "Bias tensor initialized randomly\n",
      "---------------------------------------\n",
      " [-0.37346724  0.02362406  1.29331219 -1.49729109  0.53604829 -0.24633154\n",
      "  1.41147387  0.33202285 -0.50930274 -0.37297449 -0.306416    0.9193725\n",
      " -0.20002417 -0.02619566 -0.80926347  1.9486109  -0.90745801  0.28909004\n",
      " -1.2186532  -0.24557228 -0.30858764  1.62277281 -0.02788344 -1.0173763\n",
      " -1.07106972]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    w=sess.run(weights['hidden_layer'])\n",
    "    b=sess.run(biases['hidden_layer'])\n",
    "print(\"Weight tensor initialized randomly\\n---------------------------------------\\n\",w)\n",
    "print(\"Bias tensor initialized randomly\\n---------------------------------------\\n\",b)\n",
    "sess.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input data as placeholder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf Graph input\n",
    "x = tf.placeholder(\"float32\", [None,n_input])\n",
    "y = tf.placeholder(\"float32\", [None,n_output])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden and output layers definition (using TensorFlow mathematical functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hidden layer with RELU activation\n",
    "layer_1 = tf.add(tf.matmul(x, weights['hidden_layer']),biases['hidden_layer'])\n",
    "layer_1 = tf.nn.relu(layer_1)\n",
    "\n",
    "# Output layer with linear activation\n",
    "ops = tf.add(tf.matmul(layer_1, weights['out']), biases['out'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent optimizer for training (backpropagation):\n",
    "For the training of the neural network we need to perform __backpropagation__ i.e. propagate the errors, calculated by this cost function, backwards through the layers all the way up to the input weights and bias in order to adjust them accordingly (minimize the error). This involves taking first-order derivatives of the activation functions and applying chain-rule to ___'multiply'___ the effect of various layers as the error propagates back.\n",
    "\n",
    "You can read more on this here: [Backpropagation in Neural Network](https://en.wikipedia.org/wiki/Backpropagation)\n",
    "\n",
    "Fortunately, TensorFlow already implicitly implements this step i.e. **takes care of all the chained differentiations for us**. All we need to do is to specify an Optimizer object and pass on the cost function. Here, we are using a **Gradient Descent Optimizer**.\n",
    "\n",
    "Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point.\n",
    "\n",
    "You can read more on this: [Gradient Descent](https://en.wikipedia.org/wiki/Gradient_descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define loss and optimizer\n",
    "cost = tf.reduce_mean(tf.squared_difference(ops,y))\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TensorFlow Session for training and loss estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████████████████████████████████████| 100000/100000 [00:46<00:00, 2130.28it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "import time\n",
    "\n",
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Empty lists for book-keeping purpose\n",
    "epoch=0\n",
    "log_epoch = []\n",
    "epoch_count=[]\n",
    "acc=[]\n",
    "loss_epoch=[]\n",
    "\n",
    "# Launch the graph and time the session\n",
    "t1=time.time()\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)    \n",
    "    # Loop over epochs\n",
    "    for epoch in tqdm(range(training_epochs)):\n",
    "        # Run optimization process (backprop) and cost function (to get loss value)\n",
    "        _,l=sess.run([optimizer,cost], feed_dict={x: X_train, y: y_train})\n",
    "        loss_epoch.append(l) # Save the loss for every epoch        \n",
    "        epoch_count.append(epoch+1) #Save the epoch count\n",
    "       \n",
    "        # print(\"Epoch {}/{} finished. Loss: {}, Accuracy: {}\".format(epoch+1,training_epochs,round(l,4),round(accu,4)))\n",
    "        #print(\"Epoch {}/{} finished. Loss: {}\".format(epoch+1,training_epochs,round(l,4)))\n",
    "    w=sess.run(weights)\n",
    "    b = sess.run(biases)\n",
    "    yhat=sess.run(ops,feed_dict={x:X_test})\n",
    "t2=time.time()\n",
    "\n",
    "time_SNN = t2-t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot loss function as training epochs progress"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e8fa8e0c18>]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ao2bWkTTts7tvBP4DWAdsBna5+1zStL+NiEc/W/27L9PCIS2YWSfgj8Bt7r47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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f8f12b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate and print root-mean-squared error and R^2 value for the fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE error of the shallow neural network: 779.363682123\n",
      "R^2 value of the shallow neural network: 0.142786064062\n"
     ]
    }
   ],
   "source": [
    "# Total variance\n",
    "SSt_SNN = np.sum(np.square(y_test-np.mean(y_test)))\n",
    "# Residual sum of squares\n",
    "SSr_SNN = np.sum(np.square(yhat-y_test))\n",
    "# Root-mean-square error\n",
    "RMSE_SNN = np.sqrt(np.sum(np.square(yhat-y_test)))\n",
    "# R^2 coefficient\n",
    "r2_SNN = 1-(SSr_SNN/SSt_SNN)\n",
    "\n",
    "print(\"RMSE error of the shallow neural network:\",RMSE_SNN)\n",
    "print(\"R^2 value of the shallow neural network:\",r2_SNN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot residuals plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e8fa89c358>]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Y2WJ3v7s7wbn7E8B+Ub/LvQn9g24inKzaYz+A+JPP4hxeov19L826VmftP2DSj8thMc8X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8fa8a1048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"Predicted vs. actual (test set) for shallow (1-hidden layer) neural network\\n\",fontsize=15)\n",
    "plt.xlabel(\"Actual values (test set)\")\n",
    "plt.ylabel(\"Predicted values\")\n",
    "plt.scatter(y_test,yhat,edgecolors='k',s=100,c='green')\n",
    "plt.grid(True)\n",
    "plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1e8fab78f98>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IZ0XxWtKvjvsjopGWp8eBHyuNcKv2JXY76QRwMNncitmJ7+Cy/R7M/r6OrItLabR16WjF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\naGZmZmZ5OVE0MzMzs7ycKJqZmZlZXv8LFl9S8suBqksAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8faadf3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.scatter(yhat,y_test-yhat,edgecolors='k',s=100,c='red')\n",
    "plt.title(\"Residual vs. fitted values for shallow (1-hidden layer) neural network\\n\",fontsize=15)\n",
    "plt.xlabel(\"\\nFitted values\",fontsize=15)\n",
    "plt.ylabel(\"Residuals: Difference between actual (test set)\\n and predicted values\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.axhline(y=0,lw=2,c='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More hidden layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hyperparameters and layers' variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.00001\n",
    "training_epochs = 35000\n",
    "\n",
    "n_input = 1  # Number of features\n",
    "n_output = 1  # Regression output is a number only\n",
    "\n",
    "n_hidden_layer_1 = 25 # Hidden layer 1\n",
    "n_hidden_layer_2 = 25 # Hidden layer 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights and bias variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Store layers weight & bias as Variables classes in dictionaries\n",
    "weights = {\n",
    "    'hidden_layer_1': tf.Variable(tf.random_normal([n_input, n_hidden_layer_1])),\n",
    "    'hidden_layer_2': tf.Variable(tf.random_normal([n_hidden_layer_1, n_hidden_layer_2])),\n",
    "    'out': tf.Variable(tf.random_normal([n_hidden_layer_2, n_output]))\n",
    "}\n",
    "biases = {\n",
    "    'hidden_layer_1': tf.Variable(tf.random_normal([n_hidden_layer_1])),\n",
    "    'hidden_layer_2': tf.Variable(tf.random_normal([n_hidden_layer_2])),\n",
    "    'out': tf.Variable(tf.random_normal([n_output]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the weights tensor of hidden layer 1: (1, 25)\n",
      "Shape of the weights tensor of hidden layer 2: (25, 25)\n",
      "Shape of the weights tensor of output layer: (25, 1)\n",
      "--------------------------------------------------------\n",
      "Shape of the bias tensor of hidden layer 1: (25,)\n",
      "Shape of the bias tensor of hidden layer 2: (25,)\n",
      "Shape of the bias tensor of output layer: (1,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of the weights tensor of hidden layer 1:\",weights['hidden_layer_1'].shape)\n",
    "print(\"Shape of the weights tensor of hidden layer 2:\",weights['hidden_layer_2'].shape)\n",
    "print(\"Shape of the weights tensor of output layer:\",weights['out'].shape)\n",
    "print(\"--------------------------------------------------------\")\n",
    "print(\"Shape of the bias tensor of hidden layer 1:\",biases['hidden_layer_1'].shape)\n",
    "print(\"Shape of the bias tensor of hidden layer 2:\",biases['hidden_layer_2'].shape)\n",
    "print(\"Shape of the bias tensor of output layer:\",biases['out'].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input data as placeholder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf Graph input\n",
    "x = tf.placeholder(\"float32\", [None,n_input])\n",
    "y = tf.placeholder(\"float32\", [None,n_output])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden and output layers definition (using TensorFlow mathematical functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hidden layer with RELU activation\n",
    "layer_1 = tf.add(tf.matmul(x, weights['hidden_layer_1']),biases['hidden_layer_1'])\n",
    "layer_1 = tf.nn.relu(layer_1)\n",
    "\n",
    "layer_2 = tf.add(tf.matmul(layer_1, weights['hidden_layer_2']),biases['hidden_layer_2'])\n",
    "layer_2 = tf.nn.relu(layer_2)\n",
    "\n",
    "# Output layer with linear activation\n",
    "ops = tf.add(tf.matmul(layer_2, weights['out']), biases['out'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent optimizer for training (backpropagation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define loss and optimizer\n",
    "cost = tf.reduce_mean(tf.squared_difference(ops,y))\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TensorFlow Session for training and loss estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 35000/35000 [00:20<00:00, 1699.30it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "import time\n",
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Empty lists for book-keeping purpose\n",
    "epoch=0\n",
    "log_epoch = []\n",
    "epoch_count=[]\n",
    "acc=[]\n",
    "loss_epoch=[]\n",
    "\n",
    "# Launch the graph and time the session\n",
    "t1=time.time()\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)    \n",
    "    # Loop over epochs\n",
    "    for epoch in tqdm(range(training_epochs)):\n",
    "        # Run optimization process (backprop) and cost function (to get loss value)\n",
    "        _,l=sess.run([optimizer,cost], feed_dict={x: X_train, y: y_train})\n",
    "        loss_epoch.append(l) # Save the loss for every epoch        \n",
    "        epoch_count.append(epoch+1) #Save the epoch count\n",
    "       \n",
    "        # print(\"Epoch {}/{} finished. Loss: {}, Accuracy: {}\".format(epoch+1,training_epochs,round(l,4),round(accu,4)))\n",
    "        #print(\"Epoch {}/{} finished. Loss: {}\".format(epoch+1,training_epochs,round(l,4)))\n",
    "    w=sess.run(weights)\n",
    "    b = sess.run(biases)\n",
    "    yhat=sess.run(ops,feed_dict={x:X_test})\n",
    "\n",
    "t2=time.time()\n",
    "time_DNN = t2-t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot loss function as training epochs progress"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e8fa62db00>]"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tAE4a3pvHp44LOZr4peQgIjFXXhn/51BXXUrj9N+9waAenfjyEVlMPW04KSm6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8f8f12e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate and print root-mean-squared error and R^2 value for the fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE error of the deep neural network: 308.205336459\n",
      "R^2 value of the deep neural network: 0.86594309056\n"
     ]
    }
   ],
   "source": [
    "# Total variance\n",
    "SSt_DNN = np.sum(np.square(y_test-np.mean(y_test)))\n",
    "# Residual sum of squares\n",
    "SSr_DNN = np.sum(np.square(yhat-y_test))\n",
    "# Root-mean-square error\n",
    "RMSE_DNN = np.sqrt(np.sum(np.square(yhat-y_test)))\n",
    "# R^2 coefficient\n",
    "r2_DNN = 1-(SSr_DNN/SSt_DNN)\n",
    "\n",
    "print(\"RMSE error of the deep neural network:\",RMSE_DNN)\n",
    "print(\"R^2 value of the deep neural network:\",r2_DNN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot residuals plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e8fa34af60>]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Ea9bA7rvH17nzHuA9RQ1IIH/vgbJqfgUwsxpCQrfQ3X8fFb9sZrtG9bsCr0Tl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\ngzozMzOzOvD/2Q3rihjzNPYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8fa5f4668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"Predicted vs. actual (test set) for deep (2-layer) neural network\\n\",fontsize=15)\n",
    "plt.xlabel(\"Actual values (test set)\",fontsize=15)\n",
    "plt.ylabel(\"Predicted values\",fontsize=15)\n",
    "plt.scatter(y_test,yhat,edgecolors='k',s=100,c='green')\n",
    "plt.grid(True)\n",
    "plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1e8fa5133c8>"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZmfVzeRJAdbJsE+D5bsZiZmZmZr2g0yZgSYcChxYVnSqp9J6/6wN7AbfVODYz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\nJEk9xgRQkiSpx5gASpIk9Zj/D+/X0RDRJLwuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8fa6acbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.scatter(yhat,y_test-yhat,edgecolors='k',s=100,c='red')\n",
    "plt.title(\"Residual vs. fitted values for deep (2-layer) neural network\\n\",fontsize=15)\n",
    "plt.xlabel(\"\\nFitted values\",fontsize=15)\n",
    "plt.ylabel(\"Residuals: Difference between actual (test set)\\n and predicted values\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.axhline(y=0,lw=2,c='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the time taken for model build/fit and the $R^2$-fit values achieved by each model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GcxmPJEnSymCuW8jeDPyyZ3ov4Piq2hI4vp2WJEkaK3OWkCW5D7AzcGBP8TOBQ9rnhwC7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\nB0TbhMYmgWXJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8fd1cf4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"Time taken for building/fitting models\\n\", fontsize=16)\n",
    "plt.ylabel(\"Time taken to build model\",fontsize=12)\n",
    "plt.xlabel(\"Various types of models\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.bar(left=[1,2,3],height=[time_linear,time_SNN,time_DNN], \n",
    "        align='center',tick_label=['Linear model with regularization','1-hidden layer NN','2-hidden layer NN'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cFziyp7yAG4F9xxWUJEmSVjR04lZVmwMkObqq9pi9kCRJkjSZoRK3JDtU1ent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\nHb/SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e8fcc750f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"$R^2$-fit values of the models\\n\", fontsize=16)\n",
    "plt.ylabel(\"$R^2$-fit value achieved by the model\",fontsize=12)\n",
    "plt.xlabel(\"Various types of models\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.bar(left=[1,2,3],height=[max(linear_sample_score),r2_SNN,r2_DNN], \n",
    "        align='center',tick_label=['Linear model with regularization','1-hidden layer NN','2-hidden layer NN'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
